Question

which of the following equations have exactly one solution?
choose all answers that apply:
a $-5x + 12 = -12x - 12$
b $-5x + 12 = 5x + 12$
c $-5x + 12 = 5x - 5$
d $-5x + 12 = -5x - 12$

Explanation:

Step1: Solve Equation A

Isolate $x$ terms first:
$-5x + 12x = -12 - 12$
$7x = -24$
$x = -\frac{24}{7}$
This has exactly 1 solution.

Step2: Solve Equation B

Isolate $x$ terms first:
$-5x - 5x = 12 - 12$
$-10x = 0$
$x = 0$
This has exactly 1 solution.

Step3: Solve Equation C

Isolate $x$ terms first:
$-5x - 5x = -5 - 12$
$-10x = -17$
$x = \frac{17}{10}$
This has exactly 1 solution.

Step4: Solve Equation D

Isolate $x$ terms first:
$-5x + 5x = -12 - 12$
$0 = -24$
This is a false statement, so no solution.

Answer:

A. $-5x + 12 = -12x - 12$, B. $-5x + 12 = 5x + 12$, C. $-5x + 12 = 5x - 5$